The proof in [1]} relies on the transport formula involving moving region. To the best of our knowledge, there has been little literature concerning the helicity preservation of weak solutions to
the compressible Euler equations (REF ). In this direction, most previous works focus on
the homogeneous incompressible Euler equations (REF ). In particular,
the study of helicity conservation for the incompressible Euler equations (REF )
was originated from
Chae's interesting works [2]}, [3]}.
In [3]}, Chae considered the preservation of the helicity of weak solutions to the Euler equations via \(\omega \) 
in spaces \( L^{3}(0,T;B^{\alpha }_{5,\infty }) \)  with \(\alpha >3\) .
Subsequently,
it is shown that \(v \in L^{r_{1}}(0,T;\dot{B}^{\alpha }_{2,q})\)  and
\(\omega \in L^{r_{2}}(0,T;\in \dot{B}^{\alpha }_{5,q})\) , with \(\alpha >3\) , \(q\in [2,\infty ]\) , \(r_1\in [2,\infty ]\) , \(r_2\in [1,\infty ]\)  and \(\frac{2}{r_{1}}+\frac{1}{r_{2}}=1\) , ensure the helicity conservation of weak solutions in [2]}. After that, Cheskidov-Constantin-Friedlander-Shvydkoy [6]} established the helicity conservation class based on the velocity \(v\)  in Onsager critical space
\(L^{3}(0,T;B^{3}_{3,c(\mathbb {N})}).\) 
